





from __future__ import annotations

import random

# Maximum size of the population.  Bigger could be faster but is more memory expensive.
snake_case_           =     200
# Number of elements selected in every generation of evolution. The selection takes
# place from best to worst of that generation and must be smaller than N_POPULATION.
snake_case_           =     50
# Probability that an element of a generation can mutate, changing one of its genes.
# This will guarantee that all genes will be used during evolution.
snake_case_           =     0.4
# Just a seed to improve randomness required by the algorithm.
random.seed(random.randint(0, 1000))






def lowerCamelCase__       (				snake_case_      :    Tuple			, snake_case_      :    Tuple			) ->							tuple[str, float]:
   __snake_case							=  len([g for position, g in enumerate(a__			) if g == main_target[position]]			)
   return (item, float(a__			))






def lowerCamelCase__       (				snake_case_      :    str			, snake_case_      :    List[str]			) ->							tuple[str, str]:
   __snake_case							=  random.randint(0			, len(a__			) - 1			)
   __snake_case							=  parent_a[:random_slice] + parent_a[random_slice:]
   __snake_case							=  parent_a[:random_slice] + parent_a[random_slice:]
   return (child_a, child_a)






def lowerCamelCase__       (				snake_case_      :    List[Any]			, snake_case_      :    Dict			) ->							str:
   __snake_case							=  list(a__			)
   if random.uniform(0			, 1			) < MUTATION_PROBABILITY:
      __snake_case							=  random.choice(a__			)
   return "".join(a__			)






def lowerCamelCase__       (				snake_case_      :    Any			, snake_case_      :    List[Any]			, snake_case_      :    Dict			, ) ->							list[str]:
   __snake_case							=  []
   # Generate more children proportionally to the fitness score.
   __snake_case							=  int(parent_a[1] * 100			) + 1
   __snake_case							=  10 if child_n >= 10 else child_n
   for _ in range(a__			):
      __snake_case							=  population_score[random.randint(0			, a__			)][0]

      __snake_case			,      __snake_case							=  crossover(parent_a[0]			, a__			)
      # Append new string to the population list.
      pop.append(mutate(a__			, a__			)			)
      pop.append(mutate(a__			, a__			)			)
   return pop






def lowerCamelCase__       (				snake_case_      :    int			, snake_case_      :    str			, snake_case_      :    Tuple = True			) ->							tuple[int, int, str]:

   if N_POPULATION < N_SELECTED:
      __snake_case							=  f"""{N_POPULATION} must be bigger than {N_SELECTED}"""
      raise ValueError(a__			)
   # Verify that the target contains no genes besides the ones inside genes variable.
   __snake_case							=  sorted({c for c in target if c not in genes}			)
   if not_in_genes_list:
      __snake_case							=  f"""{not_in_genes_list} is not in genes list, evolution cannot converge"""
      raise ValueError(a__			)

   # Generate random starting population.
   __snake_case							=  []
   for _ in range(a__			):
      population.append(''''''.join([random.choice(a__			) for i in range(len(a__			)			)]			)			)

   # Just some logs to know what the algorithms is doing.
   __snake_case			,      __snake_case							=  0, 0

   # This loop will end when we find a perfect match for our target.
   while True:
      generation += 1
      total_population += len(a__			)

      # Random population created. Now it's time to evaluate.

      # Adding a bit of concurrency can make everything faster,
      #
      # import concurrent.futures
      # population_score: list[tuple[str, float]] = []
      # with concurrent.futures.ThreadPoolExecutor(
      #                                   max_workers=NUM_WORKERS) as executor:
      #     futures = {executor.submit(evaluate, item) for item in population}
      #     concurrent.futures.wait(futures)
      #     population_score = [item.result() for item in futures]
      #
      # but with a simple algorithm like this, it will probably be slower.
      # We just need to call evaluate for every item inside the population.
      __snake_case							=  [evaluate(a__			, a__			) for item in population]

      # Check if there is a matching evolution.
      __snake_case							=  sorted(a__			, key=lambda snake_case_			: x[1]			, reverse=a__			)
      if population_score[0][0] == target:
         return (generation, total_population, population_score[0][0])

      # Print the best result every 10 generation.
      # Just to know that the algorithm is working.
      if debug and generation % 10 == 0:
         print(
             f"""\nGeneration: {generation}"""
             f"""\nTotal Population:{total_population}"""
             f"""\nBest score: {population_score[0][1]}"""
             f"""\nBest string: {population_score[0][0]}"""			)

      # Flush the old population, keeping some of the best evolutions.
      # Keeping this avoid regression of evolution.
      __snake_case							=  population[: int(N_POPULATION / 3			)]
      population.clear()
      population.extend(a__			)
      # Normalize population score to be between 0 and 1.
      __snake_case							=  [
          (item, score / len(a__			)) for item, score in population_score
      ]

      # This is selection
      for i in range(a__			):
         population.extend(select(population_score[int(a__			)]			, a__			, a__			)			)
         # Check if the population has already reached the maximum value and if so,
         # break the cycle.  If this check is disabled, the algorithm will take
         # forever to compute large strings, but will also calculate small strings in
         # a far fewer generations.
         if len(a__			) > N_POPULATION:
            break


if __name__ == "__main__":
    snake_case_           =     (
        'This is a genetic algorithm to evaluate, combine, evolve, and mutate a string!'
    )
    snake_case_           =     list(
        ' ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklm'
        'nopqrstuvwxyz.,;!?+-*#@^\'èéòà€ù=)(&%$£/\\'
    )
    snake_case_     ,						snake_case_     ,						snake_case_           =     basic(target_str, genes_list)
    print(
        F'\nGeneration: {generation}\nTotal Population: {population}\nTarget: {target}'
    )


from math import isqrt, loga


def 				lowerCAmelCase__       (			a__ )      ->list[int]:




  '''simple docstring'''

  _UpperCamelCase           =    [True] * max_number
  for i in range(2    ,     isqrt(max_number - 1 ) + 1 ):
    if is_prime[i]:
      for j in range(i**2    ,     a__    ,     a__ ):
        _UpperCamelCase           =    False

  return [i for i in range(2    ,     a__ ) if is_prime[i]]


def 				lowerCAmelCase__       (			a__ = 800_800    ,     a__ = 800_800 )      ->int:




  '''simple docstring'''

  _UpperCamelCase           =    degree * loga(a__ )
  _UpperCamelCase           =    int(a__ )
  _UpperCamelCase           =    calculate_prime_numbers(a__ )

  _UpperCamelCase           =    0
  _UpperCamelCase           =    0
  _UpperCamelCase           =    len(a__ ) - 1
  while left < right:
    while (
        prime_numbers[right] * loga(prime_numbers[left] )
        + prime_numbers[left] * loga(prime_numbers[right] )
        > upper_bound
    ):
      right -= 1
    hybrid_integers_count += right - left
    left += 1

  return hybrid_integers_count


if __name__ == "__main__":
   print(F"{solution() = }")




